the radical rational…

in search of innovative ideas with a well-balanced approach for the math classroom

Treats for Teachers (& a November Challenge)

As the day began, members of our student GRIT team began entering classrooms, handing teachers bags of treats.

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At first glance, a bag of candy.  But when you opened, you quickly realized it was more than expected.  There were slips of paper included…handwritten notes from students.

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The Student GRIT team has copied and dispersed these slips to all 1st period classes, asking each student to tell who and why they were grateful.

What a gift to read short, simple messages from some of your students / former students.

I was so grateful because it’s been a tough year.  Thank you, students for taking the time to do this for us.

They were genuine…and a treasure that has made me realize…I need to tell others thank you.  So, during the month of November, I challenge myself to write one note each day to someone to let them know they’ve made a difference to me.

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Battleships & Mines Systems Review

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I used Battleships and Mines as a review for systems.  We tested our mine coordinates today in the front lobby.

And then enjoyed the end of the week with the highlighters and blacklights.

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Rafters…Geometry

So, my dad is building a storage building.  This is the design he is using with end dimensions for his project.

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Easyrafters.com

He asks, “Can your students help me figure out the pitch of the roof? How long should I cut the rafters?  What angles do I use?”

Truth is, my dad likely already has them cut, ready to put together, but he knows there’s a bit of math involved that I might enjoy sharing with my class.

As I read the descritpion, I see this style is a regular octagon. 360° / 8 = 45°.  So the interior angle will be 135°.

When you cut your wood, do I split that angle in half?

I shared the diagram with other geometry teachers and Mr. H, our Carpentry Instructor at LC Area Technology Center.   I wanted to use the right approach/vocabulary Mr. H uses in his courses.  He replied almost immediately. 
The plan is to visit his classroom/shop area soon.

Now, how can I make this real for my students?  Thinking if I give them enough supplies, aka strips of construction paper to model planks of wood, and allow them to create an accurate model, describing processes for finding rafter lengths and angle measures.  Does that make sense?

An opportunity for some use of Trig, or at least a reason to use trig outside the classroom.

The website dad shared has different designs of rafters…which means we have a bank of problems to pull from.

A comment from Mr. H in our back and forth emails…

…one of the hardest to teach…geometry uses what I call the “back angle” measurement (I interpret as interior angle) and carpentry we use the “smaller” angle because we make the cuts at the intersections (if that makes sense)

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Mr. H shared some online tools and resources as well to explore.

http://www.blocklayer.com/Roof/GambrelEng.aspx

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Modeling Systems

Sort of a rambling post. But trying to make some sense of my thinking…

I always appreciate posts from @emergentmath.  This particular post made me pause, I had just completed the MARS task, Boomerangs, he references.  We are in the midst of our systems unit.

I used Mary & Alex ‘ s suggestions with beginning systems without the algebra.  Conversations were great, students’ strength in reasoning was evident.

I plan to use Geoff’s suggestion for a matching/sorting activity this werk for students to see the benefits of each type of tool to solve systems.

But where I struggle is with this standard:

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I am experiencing some pushback from a handful of students who are able to reason and solve a system without actually modeling it algebraically.

Their reasoning is correct.  They verify their solutions and interpret them correctly.  They can sketch a graph yet “refuse” to model as a system of equations.  I struggle because “their math” is right on.  I realize places where algebraic models can help but I honestly can’t tell them my way is better…yet the standard says…

It feels almost like I am punishing them if I make them model it algebraically.

Then I have others who are not sure where to start.  The equations model provides them a tool, yet they will not embrace it.

How do others handle this situation in your classrooms?

I use graphical, alongside a numerical table of values, with solving/verifying with the equations, letting them see their own connections eventually.

My biggest goal for systems is to provide enough modeling for students to actually “see a context” to connect/make sense of a naked system of equations.

This is where I believe skill/drill has ruined the power and beauty of math.  Finding an intersection point but what in the world does in mean?  It’s a point on a graph. Whoopee.  Why isn’t it all taught in context as a model?

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A Trip to the Capitol

Thursday was gorgeous.  A road trip north to our state capitol, Frankfort, with my husband and my superintendent.

Ashland Inc. Teacher Achievement Awards…and I was 1 of 24!!! 

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I debated on whether or not to post, but I am proud of my work in education and why not celebrate it! 
I teared up multiple times listening to the speakers.  40,000 educators in our state, over 500 nominations.  Overwhelmed to make the 24!
I am  grateful for the parent, student or colleague who took the time to nominate me. Wow. That, in itself, is such a huge honor!

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Yes, of course I was a bit disappointed I wasn’t named the Teacher of the Year, but listening to their professional biographies – I was in awe just to be recognized with them. Amazing teachers.  Easy to talk to, down to earth, simply loving what they do.

Last year’s TOY, Holly Bloodworth, shared how taking guitar lessons this past year…being a learner again, made her a better teacher.  She reminded us, sometimes with standards and testing, we forget…to keep the joy in our classrooms. 

Thank you to Ashland Inc. and Kentucky Department of Education for an amazing day being honored for doing something I love.

And a shout out to this guy…for always supporting and encouraging me.  And keeping me leveled out when I get overwhelmed.

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Congratulations to all Awardees!  Thank you for your passion for education!

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Rethinking Assessments

After my first assessment, I cut and pasted 8 problems that were missed most or even left blank and copied.  The following day, students worked in groups to complete those problems.

The conversations were great.  I attempted to ask questions of each group member to ensure they understood their peers thinking. 

As a whole class, we discussed why several had left certain problems blank. No attempt. At.All. 
It looked hard.
Too many words.
I was confused.
It didn’t make sense.

But after working on them in small groups, several shared how most were really very doable.  or at least the way ____ explained their thinking, ot made sense.  And how likely they will be to at least give effort on those “hard” problems next to me.

My issue was, when I asked them to complete a wrong answer analysis, only about half put effort into it. Some turned in nearly blank pages. Some turned in nothing at all.  An opportunity to learn/redo and nothing.  Yet when progress reports came out, they were upset to see they had only mastered 20% of the concepts.

They were upset that I wouldn’t give them points for just redoing and I was unfair because I didn’t let the entire class redo during class time.  They wanted me to assess their work (again) they had not even practiced/studied.

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My next attempt, was a group quiz – sort of modified from convo with @druinok and a post from @fnoschese and this article.   A couple of days prior to unit assessment, I gave them an overview of problems from the learni ng targets for the unit, it was an opportunity to discuss, look in their INBs, even asked questions of me.  It was quick to grade using this method Agree / disagree post-its

Somewhat better results.  But still, pushback on the redo’s.  A student was mad and asked how I expected them to remember what they had done /didn’t do on a test from the previous week.  Yes, given on a Wednesday, absent make-ups the following day, an assembly, the weekend and I passed them back on Monday. 

Round 3: Given on Friday. Stayed after school and marked each one.  Compiling My Favorite No on 4 Qs for whole – class discussion.  A mix of Qs missed most often for a quick group quiz, using the agree/disagree post-its again.  This will address majority of analysis I need from most of them, then assign remainder as HW. Final version of unit assessment following day.

I am interested to see what happens.

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More Efficient Packaging

So, we ended class with a dilemma the other day.  You know the one…Dan Meyer’s 3 ACT Popcorn Picker.

A great way to review some MS concepts.  And a little popcorn treat to boot.

This week, they’ll be assigned to redesign a container…

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…to a more efficient container.  Same volume, smaller surface area…

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…and defend their new container…

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…and write a letter (for our writing program review) to the VP of Packaging explaining how their new design can benefit the company.

Yes, it’s been around for years.  But again, a nice little review of things from a couple of years ago.

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And a few Dandy Candies Gift Wrapping to see their thinking in class.

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Reality Sometimes Bites

A needed vent of sorts…

I want to believe my classroom experiences have prepared me for many, varied experiences.  The truth is, each year is different, each class is different,  and sometimes I don’t have all the answers.

I so appreciate this post from @thatmathlady.  We have in mind what we want to see, hear and do in our classrooms, but inevitably, it comes down to the students who walk through the door.  Reading her post encouraged me.  Successful strategies from the past may not be right for the particular kiddos before us.  We must pause. Breathe.  Adjust.

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For several weeks, I’ve been struggling with a particular class.  Usually when things don’t go smoothly, I turn to my PLN or colleagues down the hall, adjust and hit the next day with a new strategy.  I can’t quite put my finger on it, but I have hit a wall with this class.  Nothing I’ve tried seems to make progress.  And I am frustrated.  You would expect a veteran teacher to know what to do.  We are nearly half way through the semester and I feel like I have failed.

Yes, there are some who are struggling, thus their outbursts of verbal frustrations.  Yet, I see no effort at all on their part to improve.  I fear by the time I begin to make some turnaround with them, the semester will be over. And it will be too late.

I suppose I place too much of my own worth/value in their progress.  I need to step back. Breathe.  Remind myself there is only so much I can do.  At some point, it’s got to be their choice to want to improve.  I have not been able to convince them I am here as their support.  They don’t trust me.  When they are ready to begin moving forward, I can provide help and direction.  Until then, I will continue to invest in all learners to the best of my ability.

I will not, however, waste valuable class time arguing over their lack of effort and desire to learn.  I have lost control because I allowed them to set the tone of the classroom.  Its disrespectful of their classmates and myself.  Its unprofessional on my part that I’ve allowed it. It’s unacceptable.

If they choose not to participate, they will not interupt myself or others of our desire to move forward.

Usually, there is 1 or 2 students who buck my classroom system, but I eventually am able to coax them from the dark side.  But this class, I have experienced disrespect from at least 7 students.  Nearly 1/3 of the class. 

I have attempted win-win conversations, how can our attitudes and actions change to make this better and work?  Even asking what I could do.  No improvements.

Sadly, the learning environment in my classroom breaks my heart.    I shouldn’t have, but I told them in 20 years, I have not experienced a more disrespectful class.  This is sad because it’s not the majority of the students.

The last day in class I was in survival mode.  I was thankful for Homecoming Picnic the following day so I didn’t have to see them.  I needed a timeout. 

This week is fall break.  A much needed break.  I have read, perused blogs, looking for an up-do.  I want to return Monday with a new attitude, new energy.  I want to believe I can still make a difference. 

The reality is, I was shaken.  It’s hard when something you adore doing turns around and bites you.  It’s difficult to face that challenge.  But I remind myself, not to give up.  It’s hard. I’m human. 

So once, again, I pull out the star fish story as a reminder…

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Department Reflection

Last year I wanted to do a task with my department, but I was afraid of what they would think, so I didn’t do it.     I kept running across a screenshot from @tjterryjo’s example. 

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I finally decided, it’s worthwhile, a good brainstorming task and would lend to a part of our teacher planning day before fall break.

It began with teachers brainstorming what they envisioned as the Dream Math Student on sticky notes.

We carouseled around the room to read others’ thoughts.  Some were quite different, but several similar.

I recorded what they shared on chart paper in green.  One idea not shared but I saw it on a sticky was enjoy mathematics. 

We then brainstormed again, what are the actions we can take as teachers to encourage these traits?  What opportunities can we provide?

Again, we carouseled to observe others, then shared and recorded on the chart.

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This snapshot will be emailed to each person.  A colleague is printing color copies for everyone to keep in their room as a reminder.

At our next PLC, we will revisit our chart and dotify with stickers the traits we are seeing in our classrooms and the actions we are taking as teachers.

As a department, we decided to pick a couple of actions we agreed everyone could focus on.  In efforts to help students not to fear failure, we will try specific feedback, purposeful praise.  Acknowledge student process and effort, steps they take in solving problems, rather than the end result, right/wrong answers.

As an attempt to motivate and build confidence, we want to help students set attainable goals.  We use interim benchmarks throughout our courses.  We have recently completed the first one.  It was suggested we prepare graphical reports for ea ch student, share them, explain the end goal, but then allow students to set their own goal for our 2nd round at the end of the semester.  We will meet with each student, helping them decide if their goal is attainable, yet provides a challenge to work for as well.

There will be a shout-out board in our hallway to acknowledge students who 1) reach their goal 2) are progressing toward their goal. 

I have extremely talented colleagues who work hard and want their student’s to experience success.  Yet it can be frustrating when we don’t see progress we would like.  I think this conversation began a cycle of reflection where can can begin trying different strategies and adjust in some of our approaches than may provide better learning experiences for our students, helping them move forward.

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Fall Break Begins with Pumpkin Pancakes

I love fall. 
Cool mornings and mild afternoons are my favorite. 
I was in the mood for pancakes this morning. Since my 10 year old has talked about her Pumpkin Roll Marathon at Gramma’s last weekend (my mom makes enough in one day for all fall family holiday dinners, then freezes them), well… I was in the mood for pumpkin, too.

I gave it a try.

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Pumpkin Pancakes
1 cup buttermilk*
1 – 1 1/4 cup self rising flour
1/4 cup pumpkin
1 TBSP honey
1 tsp vanilla
Stir until well blended. Cook in sprayed/buttered hot skillet.
Makes 6-8 6″ pancakes.

Sweet Cream Cheese Butter
2 oz. cream cheese, room temp
1 oz. Butter, room temp
2 TBsp. Confectioner’s sugar
Blend well. Dollop onto hot pancake.

Fast Salted Caramel Sauce
In sauce pan, heat 2 oz butter with 1/4 cup brown sugar and 2 TBsp milk or cream until melted and smooth.  Add sea salt to taste. Drizzle over pancakes. 

Optional: sprinkle with toasted pecans or walnuts.

*add 1 TBSP white vinegar to 1 cup milk, let it sit a few minutes to ‘sour’ milk

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